0

I would suspect that a financial maths book would introduce the following, but I am only a novice and so would cherish your recommendations. The following is motivated by pp 304-305, ETFs for Canadians for Dummies (2013; by Russell Wild and Bryan Borzykowski). (which only invokes arithmetic and no further maths). Please simply recommend resources if any answers my question. Denote:
$D$ = Dollar value of your current portfolio
$S_i$ = Dollar value of financial instrument $i$ (eg a common stock)
$p_i$ = Proportion of your portfolio in $S_i$, where $0 \le p_i \le 1$.
Thus $ D= \sum_{1 \le i \le n} p_iS_i$.

You desire to change your portfolio by amount $C$, and desire your changed portfolio to become:

$D + C = \sum_{1 \le i \le n} p_i'S_i'$. You decide and so know $p_i'$, but how do you solve for $S_i'$ for each $i$?

  • Has the choice of the $n$ financial instruments changed? If not, they have the same value as before, don't they? So isn't $S'_i=S_i$? – MPW Sep 17 '15 at 01:31
  • This may need some clarification: The market tells you the price of each instrument. Hence, the market hands you each $S_i'$, these might differ from the original prices because prices change from day to day. The portion in each asset is something you select. I believe $D$ must mean the dollar value of one unit of your portfolio...not the entire value, no? – lulu Sep 17 '15 at 01:33
  • As a concrete example: suppose you had two stocks, $A$ and $B$. one share of $A$ costs $$1$, say while one share of $B$ costs $$3$. You decide you want $p_A=p_B=\frac 12$. Thus one (formal) unit of your preferred portfolio costs the average, $$2$. If you had $$100$ to invest you could buy $50$ units of your portfolio, hence $25$ shares of each stock. – lulu Sep 17 '15 at 01:44
  • @lulu Please advise if I should consider the dollar value of one unit of your portfolio, but I did mean the entire value of the portfolio. So in your concrete example, $D = $100$. –  Sep 17 '15 at 02:36
  • @MPW You are correct that the $n$ financial instruments have remained the same stocks as before, but their value might have changed because $S_i$ precedes $S_i'$ in time. –  Sep 17 '15 at 02:37
  • Well, if D means the total, then I don't understand what the other variables mean. Perhaps I am misreading but I took the $S_i$ to mean the market price of a unit of asset $i$. Thus it was the share price of a stock, say. The $p_i$ are then percents. If, instead, $S_i$ meant the total dollar value of whatever you own of asset $i$ then your total dollar amount would be the (unweighted) sum of the $S_i$. – lulu Sep 17 '15 at 09:31
  • Thanks. You are correct that I intended $S_i$ to mean meant the total dollar value of whatever you own of asset $i$. Does this clarify? –  Sep 17 '15 at 18:50

0 Answers0